and not just because of egg allergies that affect about 2% of children and persist in about half of adults that showed it in childhood.
Vaccines grown in eggs develop antibodies, not only to the organism targeted (e.g., flu virus) but to sugar molecule found in eggs, thereby shifting the antibody response intended and thus diminishing immunity. Further, a process known as egg adaptation can result in mutations in the target virus itself and ultimately diminished immunogenicity. This has been a major factor in flu vaccine failures--depending on the original circulating prominent virus type. For example virus effectiveness has been shown to be dramatically lower for egg-grown vaccines against influenza A (H3N2) than influenza A (H1N1) and influenza B viruses.
https://www.sciencedirect.com/science/article/pii/S1931312819302574
So, while egg-based COVID-19 viruses are possible it is not reasonable to think these same issues would not be at play--particularly given how mutation-prone these Coronaviruses have been shown to be. So, I don't see that as a likely path to better or even cheaper vaccines for the third world (mammalian cell culture MIGHT be an option, however).